On the degree of caustics of reflection

Details On the degree of caustics of reflection On the degree of caustics of reflection

2012-01-03

arxiv.org/abs/1201.0621v1

Mathematics

Algebraic Geometry

35 pages, 1 figure

Scientific paper

Given a point S and an irreducible algebraic curve C in P^2, we consider the caustic of reflection defined as the envelope of the reflected lines from the point S on the curve C. We identify this caustic with the Zariski closure of the image of C by a rational map. Thanks to a general fundamental lemma, we give a formula of the degree of the caustic of reflection in terms of multiplicity numbers of pro-branches of C. Our formula holds in the most general case. We also give some precisions about Pl\"ucker formulas.

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